Well, as I was listening to it, it occurred to me that, while "Bob Dylan" was released in 1962, it was recorded in 1961, the year of my birth. 1961 was the year that John Hammond signed Dylan to a recording contract after seeing him perform in the clubs of lower Manhattan, where Dylan lived after leaving Minnesota.
That same year, on the other side of the ocean, a young British fan happened to walk into a Liverpool record shop to ask the proprietor, Brian Epstein, if he had any copies of the song "My Bonnie," which had been recorded by the then relatively unknown Beatles; Epstein sought the band out, a year later they had a recording contract, and the rest is history.
1961 was the year that a charismatic young president took office; the hopes and dreams of America, and indeed, the world, for peace, freedom, and equality, which were projected onto and associated with Kennedy and Camelot were not unlike the ideals that were associated with the songs of Bob Dylan, particularly those which offered social and political commentary; also, it has been suggested by many that the emergence of the Beatles in America a few years later in 1964 was a means of helping a grieving nation to get over some of its grief and to start feeling happy again. In any event, the 60s were by then well under way.
Thinking back a tad earlier than this, to a time prior to my birth, and to pop culture and its reception, in the 1950s, it occurs to me that at least some (upper middle class) college students certainly did tend to gravitate toward smooth sounding, relatively bland folk-pop, as well as - based on a reliable source with whom I regularly chat - such cool jazz acts as Dave Brubeck and Cal Tjader; their more blue collar, working class counterparts in the 50s - such as my parents and their friends, they tended to lean toward whatever commercial pop stuff was played on the radio, as it would make sense that they would; I never knew my parents to listen to Brubeck or the Kingston Trio. While I wasn't around to experience the 50s, from what I've read, it was only a relatively small counterculture of clued-in folks who would have been reading Jack Kerouac, Lawrence Ferlinghetti, and William Burroughs (which I did, a few decades later), listening to more radical forms of music, and actively opposing McCarthyism. I'd like to think that that's where I would have been had I been an adult member of 1950s American society, but who knows?
Let me close with a bit of a beloved jazz figure and something that also came out in the year of my birth.